Stretch each ball of dough into a 12-in. round and place on a lightly oiled sheet of parchment paper. Flip each dough round onto preheated grill, then remove parchment paper. Grill, covered, until dough puffs, about 2 minutes. Transfer rounds to a baking sheet, grilled sides up.

Step 5

Sprinkle grilled side of each round with 1 cup cheese, then half of onion mixture and half of remaining cheese. Using a wide spatula, transfer pizzas to grill and cook, covered, 1 to 2 minutes; then pop any large bubbles (this keeps the pizza fairly flat so toppings stay on). Cook until browned and crisp on bottoms, 3 to 5 minutes more. Remove pizzas from grill and sprinkle with chives.